{"id":1286,"date":"2023-06-22T02:13:18","date_gmt":"2023-06-22T02:13:18","guid":{"rendered":"https:\/\/content.one.lumenlearning.com\/introstatstest\/chapter\/t-distribution-apply-it-1\/"},"modified":"2025-05-16T03:59:58","modified_gmt":"2025-05-16T03:59:58","slug":"t-distribution-apply-it-1","status":"publish","type":"chapter","link":"https:\/\/content.one.lumenlearning.com\/introstatstest\/chapter\/t-distribution-apply-it-1\/","title":{"raw":"t-distribution: Apply It 1","rendered":"t-distribution: Apply It 1"},"content":{"raw":"<section class=\"textbox learningGoals\">\r\n<ul>\r\n\t<li><span data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;Check the conditions for a t-distribution, then use a t-distribution to calculate probabilities when appropriate&quot;}\" data-sheets-userformat=\"{&quot;2&quot;:4865,&quot;3&quot;:{&quot;1&quot;:0},&quot;11&quot;:3,&quot;12&quot;:0,&quot;15&quot;:&quot;Calibri&quot;}\">Check the conditions for a [latex]t[\/latex]-distribution, then use a [latex]t[\/latex]-distribution to calculate probabilities when appropriate.<\/span><\/li>\r\n<\/ul>\r\n<\/section>\r\n<p><img class=\"alignright wp-image-577\" src=\"https:\/\/content-cdn.one.lumenlearning.com\/wp-content\/uploads\/sites\/10\/2022\/11\/23211649\/Picture1-6.jpg\" alt=\"A barista behind the counter of a coffee shop.\" width=\"264\" height=\"177\" \/><\/p>\r\n<h2>Working Through College<\/h2>\r\n<p>Many undergraduate students are employed at the same time they are enrolled in school. In 2020, the National Center for Education Statistics reported that [latex]40\\%[\/latex] of full-time students worked.[footnote]U.S. Department of Education, Institute of Education Sciences, National Center for Education Statistics. (2020). College student employment. Retrieved from https:\/\/nces.ed.gov\/programs\/coe\/indicator\/ssa\/college-student-employment[\/footnote] Being employed while in school can help a student pay for tuition, housing, and other expenses, but it can also be associated (either positively or negatively) with a student\u2019s academic performance.<\/p>\r\n<section class=\"textbox tryIt\">[ohm2_question hide_question_numbers=1]969[\/ohm2_question]<\/section>\r\n<p>A random sample of [latex]15[\/latex] employed full-time students at a large university was selected for a survey on employment. The following is the number of hours (in increasing order) worked per week for each of those [latex]15[\/latex] students:<\/p>\r\n<p style=\"text-align: center;\">2\u00a0 \u00a05 \u00a0\u00a07 \u00a010 \u00a016 \u00a019 \u00a019 \u00a022 \u00a023 \u00a026 \u00a027 \u00a027 \u00a031 \u00a040 \u00a050<\/p>\r\n<section class=\"textbox interact\"><strong>Step 1: <\/strong>Select <strong>Your Own<\/strong>\u00a0under <strong>Enter Data<\/strong>.<br \/>\r\n<strong>Step 2:<\/strong> Enter a descriptive name for the variable (e.g., Hours Worked per Week).<br \/>\r\n<strong style=\"font-size: 1rem; orphans: 1; text-align: initial; background-color: initial; word-spacing: normal;\">Step 3:<\/strong><span style=\"font-size: 1rem; orphans: 1; text-align: initial; background-color: initial; word-spacing: normal;\"> Copy and paste the observations above into the statistical tool.<\/span><\/section>\r\n<p><iframe src=\"https:\/\/lumen-learning.shinyapps.io\/eda_quantitative\/ \" width=\"100%\" height=\"900\" frameborder=\"no\"><span data-mce-type=\"bookmark\" style=\"display: inline-block; width: 0px; overflow: hidden; line-height: 0;\" class=\"mce_SELRES_start\"><\/span><\/iframe><br \/>\r\n[<a href=\"https:\/\/lumen-learning.shinyapps.io\/eda_quantitative\/\" target=\"_blank\" rel=\"noopener\">Trouble viewing? Click to open in a new tab.<\/a>]<\/p>\r\n<section class=\"textbox tryIt\">[ohm2_question hide_question_numbers=1]1795[\/ohm2_question]<\/section>","rendered":"<section class=\"textbox learningGoals\">\n<ul>\n<li><span data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;Check the conditions for a t-distribution, then use a t-distribution to calculate probabilities when appropriate&quot;}\" data-sheets-userformat=\"{&quot;2&quot;:4865,&quot;3&quot;:{&quot;1&quot;:0},&quot;11&quot;:3,&quot;12&quot;:0,&quot;15&quot;:&quot;Calibri&quot;}\">Check the conditions for a [latex]t[\/latex]-distribution, then use a [latex]t[\/latex]-distribution to calculate probabilities when appropriate.<\/span><\/li>\n<\/ul>\n<\/section>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignright wp-image-577\" src=\"https:\/\/content-cdn.one.lumenlearning.com\/wp-content\/uploads\/sites\/10\/2022\/11\/23211649\/Picture1-6.jpg\" alt=\"A barista behind the counter of a coffee shop.\" width=\"264\" height=\"177\" \/><\/p>\n<h2>Working Through College<\/h2>\n<p>Many undergraduate students are employed at the same time they are enrolled in school. In 2020, the National Center for Education Statistics reported that [latex]40\\%[\/latex] of full-time students worked.<a class=\"footnote\" title=\"U.S. Department of Education, Institute of Education Sciences, National Center for Education Statistics. (2020). College student employment. Retrieved from https:\/\/nces.ed.gov\/programs\/coe\/indicator\/ssa\/college-student-employment\" id=\"return-footnote-1286-1\" href=\"#footnote-1286-1\" aria-label=\"Footnote 1\"><sup class=\"footnote\">[1]<\/sup><\/a> Being employed while in school can help a student pay for tuition, housing, and other expenses, but it can also be associated (either positively or negatively) with a student\u2019s academic performance.<\/p>\n<section class=\"textbox tryIt\"><iframe loading=\"lazy\" id=\"ohm969\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=969&theme=lumen&iframe_resize_id=ohm969&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n<p>A random sample of [latex]15[\/latex] employed full-time students at a large university was selected for a survey on employment. The following is the number of hours (in increasing order) worked per week for each of those [latex]15[\/latex] students:<\/p>\n<p style=\"text-align: center;\">2\u00a0 \u00a05 \u00a0\u00a07 \u00a010 \u00a016 \u00a019 \u00a019 \u00a022 \u00a023 \u00a026 \u00a027 \u00a027 \u00a031 \u00a040 \u00a050<\/p>\n<section class=\"textbox interact\"><strong>Step 1: <\/strong>Select <strong>Your Own<\/strong>\u00a0under <strong>Enter Data<\/strong>.<br \/>\n<strong>Step 2:<\/strong> Enter a descriptive name for the variable (e.g., Hours Worked per Week).<br \/>\n<strong style=\"font-size: 1rem; orphans: 1; text-align: initial; background-color: initial; word-spacing: normal;\">Step 3:<\/strong><span style=\"font-size: 1rem; orphans: 1; text-align: initial; background-color: initial; word-spacing: normal;\"> Copy and paste the observations above into the statistical tool.<\/span><\/section>\n<p><iframe loading=\"lazy\" src=\"https:\/\/lumen-learning.shinyapps.io\/eda_quantitative\/\" width=\"100%\" height=\"900\" frameborder=\"no\"><span data-mce-type=\"bookmark\" style=\"display: inline-block; width: 0px; overflow: hidden; line-height: 0;\" class=\"mce_SELRES_start\"><\/span><\/iframe><br \/>\n[<a href=\"https:\/\/lumen-learning.shinyapps.io\/eda_quantitative\/\" target=\"_blank\" rel=\"noopener\">Trouble viewing? Click to open in a new tab.<\/a>]<\/p>\n<section class=\"textbox tryIt\"><iframe loading=\"lazy\" id=\"ohm1795\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=1795&theme=lumen&iframe_resize_id=ohm1795&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n<hr class=\"before-footnotes clear\" \/><div class=\"footnotes\"><ol><li id=\"footnote-1286-1\">U.S. Department of Education, Institute of Education Sciences, National Center for Education Statistics. (2020). College student employment. Retrieved from https:\/\/nces.ed.gov\/programs\/coe\/indicator\/ssa\/college-student-employment <a href=\"#return-footnote-1286-1\" class=\"return-footnote\" aria-label=\"Return to footnote 1\">&crarr;<\/a><\/li><\/ol><\/div>","protected":false},"author":8,"menu_order":18,"template":"","meta":{"_candela_citation":"[]","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"part":1268,"module-header":"apply_it","content_attributions":[],"internal_book_links":[],"video_content":null,"cc_video_embed_content":{"cc_scripts":"","media_targets":[]},"try_it_collection":null,"_links":{"self":[{"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapters\/1286"}],"collection":[{"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/users\/8"}],"version-history":[{"count":7,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapters\/1286\/revisions"}],"predecessor-version":[{"id":6790,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapters\/1286\/revisions\/6790"}],"part":[{"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/parts\/1268"}],"metadata":[{"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapters\/1286\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/media?parent=1286"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapter-type?post=1286"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/contributor?post=1286"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/license?post=1286"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}